in this paper, we first introduce the notion of $c$-affine functions for $c> 0$.then we deal with some properties of strongly convex functions in real inner product spaces by using a quadratic support function at each point which is $c$-affine. moreover, a hyers–-ulam stability result for strongly convex functions is shown.

In this paper, we consider the following problem: maxx∈D{ ∑m j=1 gj(x)/hj(x)}, where gj(x) ≥ 0 and hj (x) > 0, j = 1, · · · ,m are d.c. (difference of convex) functions over a convex compact set D in Rn. We reformulate it into a problem of maximizing a linear objective function over a feasible region defined by multiple reverse convex functions. Several favorable properties are presented and a ...

The concept of convex polygon-offset distance function was introduced in 2001 by Barequet, Dickerson, and Goodrich. Using this notion of point-to-point distance, they showed how to compute the corresponding nearestand farthest-site Voronoi diagram for a set of points. In this paper we generalize the polygon-offset distance function to be from a point to any convex object with respect to an m-si...

We consider the behavior of a 2-level storage system operating with the LRU or the FIFO replacement strategy where accesses to the main storage are described by the independent reference model (IRM). Let the size of main storage be m. We prove that the miss ratio (i.e. the steady-state probability that the item currently required is not in main storage) exhibits the following properties: The mi...

In this paper, we establish some Hermite-Hadamard type inequalities for function whose n-th derivatives are logarithmically convex by using Riemann-Liouville integral operator.

The analysis of flow in water-distribution networks with several pumps by the Content Model may be turned into a non-convex optimization uncertain problem with multiple solutions. Newton-based methods such as GGA are not able to capture a global optimum in these situations. On the other hand, evolutionary methods designed to use the population of individuals may find a global solution even for ...

We study the problem of finding an optimal kernel from a prescribed convex set of kernels K for learning a real-valued function by regularization. We establish for a wide variety of regularization functionals that this leads to a convex optimization problem and, for square loss regularization, we characterize the solution of this problem. We show that, although K may be an uncountable set, the ...

In this paper, we study integral inequalities which will provide refinements of bounds unified operators established for convex and α , m -convex functions. A new definition function, namely, strongly id="M3"> function is applied in different forms ...

The main aim of this paper is to give refinement bounds fractional integral operators involving extended generalized Mittag-Leffler functions. A new definition, namely, strongly α , m -convex function introduced obtain improvements fo...